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Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres

Tom 93 / 2011

Elmar Wagner Banach Center Publications 93 (2011), 225-240 MSC: Primary 58B34; Secondary 17B37. DOI: 10.4064/bc93-0-18

Streszczenie

It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2) and it is shown that the failure of the real structure to satisfy the commutant property is related to the failure of the universal R-matrix operator to be unitary.

Autorzy

  • Elmar WagnerInstitute of Physics and Mathematics
    Michoacan University of San Nicolás of Hidalgo
    Morelia, Mexico
    e-mail

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